Pith Number

pith:CFFLFCO6

pith:2015:CFFLFCO63A2XG7JSXFN6J3O22P

not attested not anchored not stored refs pending

An upper bound for the probability of visiting a distant point by critical branching random walk in $\mathbb{Z}^4$

Qingsan Zhu

arxiv:1503.00305 v2 · 2015-03-01 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CFFLFCO63A2XG7JSXFN6J3O22P}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:56:38.268993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

114ab289ded835737d32b95be4eddad3dadbcdee284f03902536afc0e3ddc68d

Aliases

arxiv: 1503.00305 · arxiv_version: 1503.00305v2 · doi: 10.48550/arxiv.1503.00305 · pith_short_12: CFFLFCO63A2X · pith_short_16: CFFLFCO63A2XG7JS · pith_short_8: CFFLFCO6

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CFFLFCO63A2XG7JSXFN6J3O22P \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 114ab289ded835737d32b95be4eddad3dadbcdee284f03902536afc0e3ddc68d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9c609bc30c761bd3e762feafa846dc055aa32801e7c34eb92b4d382676ea5a1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-03-01T16:50:34Z",
    "title_canon_sha256": "d34a388b3443b9be8e697b3f703c07fc2edb4e46986bed81728f4f7fe292c61e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.00305",
    "kind": "arxiv",
    "version": 2
  }
}